In many areas of science and technology, there exists a need to determine the concentration of chemical substances in small samples. One method for determining the concentration of a substance is quantitative microspectroscopy. In this case one measures the optical absorbance, A(.lambda.,c), which is related to the concentration, c, via the simple equation (1): EQU A(.lambda.,c)=a(.lambda.)cz (1)
where .lambda. is the optical wavelength, a(.lambda.) is the wavelength-dependent absorption coefficient, and z is the sample thickness.
The error in determining the concentration is given by equation (2): ##EQU1##
The error in the absorbance measurement can be kept extremely low, using modern optoelectronics and electronics equipment. For a given substance, the absorption coefficient, a(.lambda.), can be determined precisely in advance by using large samples with a thickness in the range 1 mm to 10 mm. Consequently, the error in determining the concentration, c, in small samples having a thickness in the sub-mm range is dominated by the error in measuring the sample thickness, and is given by equation (3): ##EQU2##
From equation (3) it follows that determining the concentration of a chemical substance within a 10 .mu.m thick microsample with an accuracy of 1% would require knowledge of the sample thickness with an accuracy of 1%, i.e. with an accuracy of 100 nm.
Producing microsample containers with a precision in the sample thickness of 100 nm might be possible, but is expected to be cost-intensive. Moreover, such microsample containers are likely to deform over their shelf life during storage, or to deform due to sample loading. It is apparent that it is practical to determine the exact sample thickness at the time of usage, after loading the sample into the container. Consequently, there exists a need for a method and apparatus for precisely determining the thickness of thin optical samples.